Problem: What number could replace $r$ below? $\dfrac{3}{10} = \dfrac{30}{r}$
Explanation: The fraction on the left represents 3 out of 10 slices of a rectangular cake. How many total slices would we need if we want the same amount of cake in 30 slices? We would need to cut the cake into 100 slices. $\dfrac{3}{10} = \dfrac{30}{100}$ and so the answer is $100$ Another way to get the answer is to multiply by $\dfrac{10}{10}$ $\dfrac{10}{10} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{3}{10} \times \dfrac{10}{10} = \dfrac{30}{100} $ so our answer is $100$.